The disclosed technology relates generally to bandwidth efficient communications or storage systems, and more particularly, to systems and methods for encoding and decoding signal vectors based on a fractional signaling scheme in a bandwidth efficient communications or storage system.
To improve the reliability of communications and storage systems, error control coding is commonly applied to the information that is conveyed or stored. A suitable error correcting code (ECC) can be applied to the information, which adds redundancy to the data stream. If the same throughput of information or storage space is desired in communication/storage, bandwidth expansion is often necessary. Bandwidth expansion refers to an increase in channel bandwidth, typically to allow transmission or storage to occur through the channel with a reduced symbol period or increased storage density. For some channels, especially for those that are low in quality, bandwidth expansion may not be possible or may not be desirable. In these situations, rather than increasing the needed bandwidth, the communication or storage system can utilize modulation schemes with a greater number of signal constellation points. For communications systems, this technique allows for more information to be transmitted at any given time. For example, signaling schemes that double the number of signal constellation points used for transmission, which therefore doubles the amount of information transmitted each symbol period, may produce substantially the same throughput as a signaling scheme that maintains the modulation scheme and doubles the channel bandwidth.
To fully utilize the advantages provided by increasing the number of signal constellation points, the type of modulation and the type of error correcting code should be designed to operate effectively together. This type of data encoding is typically referred to as coded modulation. When a convolutional code is used for the error correcting code, the system implements trellis coded modulation (TCM), and when a block code is used, the system implements block coded modulation (BCM).
However, by increasing the number of signal constellation points, neighboring signal constellation points may be brought closer together. For example, the voltage difference between neighboring signal constellation points may be made relatively small as signal constellation points are added to the modulation scheme. Therefore, the communications or storage system may be more susceptible to channel noise and other disturbances.